Does playing a Sand Soldier with Emperor's Dais trigger Legion for Noxus Hopeful?

No. Playing a Sand Soldier token from Emperor's Dais does not satisfy the Legion condition for Noxus Hopeful.

Legion (Rule 812.1.c) requires "a card different than the one with the Legion ability" to have been finalized that turn. Tokens are not cards (Rule 182). A Sand Soldier is a token unit (Rule 184.3) — it can trigger "when you play a unit" effects like Rengar's legend, but it doesn't count as "playing a card" for Legion. You'd need to play an actual card from your hand first to unlock Noxus Hopeful's discount.